Two- and three-dimensional numerical simulations are performed to study interfacial waves in a periodic domain by imposing a source term in the horizontal momentum equation. Removing the source term before breaking generates a stable interfacial wave. Continued forcing results in a two-dimensional shear instability for waves with thinner interfaces, and a convective instability for waves with thick interfaces. The subsequent three-dimensional dynamics and mixing is dominated by secondary cross-stream convective rolls which account for roughly half of the total dissipation of wave energy. Dissipation and mixing are maximized when the interface thickness is roughly the same size as the amplitude of the wave, while the mixing efficiency is a weak function of the interface thickness. The maximum instantaneous mixing efficiency is found to be $0.36\pm 0.02$.